MATA23H3 Lecture Notes - Lecture 8: Elementary Matrix, Augmented Matrix, European Route E40
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Mata23 - lecture 8 - consistency, inverses, and elementary row matrices. Consistency: a linear system having no solutions is inconsistent. If it has one or more solutions, the linear system is said to be consistent: let a(cid:126)x = (cid:126)b be a system with a mm,n(r). 2x + 9y + z = : example 9: discuss the solutions of. 0: ( + 7 = 0) ( = 7) 0: + 7 (cid:54)= 0, rank h = rank g = 3 = n. (( + 7)z = 18) (z = + 7 x + 4y 2z = 4. + 7 x = 36 10. (cid:126)a1x1 + + (cid:126)anxn = (cid:126)b. Determine whether or not (cid:126)y belongs to sp((cid:126)v1, (cid:126)v2, (cid:126)v3) Sp((cid:126)v1, (cid:126)v2, (cid:126)v3) = {x1(cid:126)v1 + x2(cid:126)v2 + x3(cid:126)v3|xi r, i = 1, 2, 3} X1(cid:126)v1 + x2(cid:126)v2 + x3(cid:126)v3 = (cid:126)y. Multiply row i by c (cid:54)= 0. Add c times row i to row j.
